Linear Wakefield Expression For Bi-Gaussian Drive Bunches

INTRODUCTION This is a brief note whose purpose is to clarify some confusion in the literature regarding the prediction of linear theory for the wakes produced by narrow particle beam bunches. By narrow, we mean the beam’s spot size is small compared to the collisionless skin depth. In linear theory there is not difference in the wake amplitude between electron and positron bunches (although there is a change in sign in the wake). We concentrate on bi-Gaussian shaped bunches. In a manuscript under preparation we give more details on the theory and discuss the validity of the linear predictions as the bunch charge is increased.